CAGR (Compound Annual Growth Rate): Definition, Formula & Calculator
Compound Annual Growth Rate (CAGR) is the mean annual growth rate of an investment over a specified period longer than one year. It represents one of the most accurate ways to calculate and communicate the returns of anything that can increase or decrease in value over time.
Table of Contents
What Is CAGR?
CAGR, or Compound Annual Growth Rate, is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR isn't the actual return in any given year. Rather, it's a representational figure that describes the rate at which an investment would have grown if it had grown at the same rate every year and the profits were reinvested at the end of each year.
Think of CAGR as the "smoothed" rate of growth that, if applied consistently over the entire investment period, would yield the same final value as the actual investment with its ups and downs.
Example:
If your portfolio grew from $10,000 to $16,105 over 5 years, the CAGR would be 10% - meaning your investment grew at an average compound rate of 10% per year, even if individual years saw different returns.
Understanding Compound Growth
Compound growth is the process where an asset's earnings are reinvested to generate additional earnings over time. This growth occurs because the investment generates earnings from both its initial principal and the accumulated earnings from preceding periods.
The Power of Compounding
Albert Einstein allegedly called compound interest "the eighth wonder of the world," and for good reason. Compound growth accelerates wealth accumulation because you earn returns not just on your original investment, but also on all the gains that investment has already produced.
Note: The key difference between simple growth and compound growth is that compound growth assumes reinvestment of returns, leading to exponential rather than linear growth over time.
Compound Growth in Action
Consider an investment of $1,000 growing at 10% annually:
| Year | Starting Value | Growth (10%) | Ending Value |
|---|---|---|---|
| 1 | $1,000 | $100 | $1,100 |
| 2 | $1,100 | $110 | $1,210 |
| 3 | $1,210 | $121 | $1,331 |
| 4 | $1,331 | $133 | $1,464 |
| 5 | $1,464 | $146 | $1,610 |
Notice how the growth amount increases each year? That's compound growth in action - you're earning returns on your returns.
The CAGR Formula
CAGR Formula
CAGR = (Ending Value / Beginning Value)^(1/n) - 1 Where: • Ending Value = Final value of the investment • Beginning Value = Initial value of the investment • n = Number of years
This formula essentially calculates the nth root of the total return, then subtracts 1 to convert it to a percentage rate.
Alternative Formula Representation
The CAGR formula can also be expressed as:
CAGR = [(FV/PV)^(1/n)] - 1Where FV is Future Value and PV is Present Value.
How to Calculate CAGR
Let's walk through calculating CAGR step by step with a real example:
Example Calculation:
Suppose you invested $5,000 in a stock in 2020, and by 2024 it was worth $8,500.
- Identify your values:
- Beginning Value: $5,000
- Ending Value: $8,500
- Number of years: 4
- Calculate the ratio: $8,500 ÷ $5,000 = 1.7
- Take the nth root: 1.7^(1/4) = 1.7^0.25 = 1.1412
- Subtract 1: 1.1412 - 1 = 0.1412
- Convert to percentage: 0.1412 × 100 = 14.12%
The CAGR is 14.12%, meaning the investment grew at an average compound rate of 14.12% per year.
CAGR Calculator
Calculate Your CAGR
CAGR vs Average Annual Return
One of the most common mistakes investors make is confusing CAGR with average annual return. These two metrics can tell very different stories about the same investment.
Key Differences
| Aspect | CAGR | Average Annual Return |
|---|---|---|
| Calculation Method | Geometric mean | Arithmetic mean |
| Accounts for Compounding | Yes | No |
| Volatility Impact | Smooths out volatility | Ignores volatility effects |
| Real Return Representation | More accurate | Can be misleading |
Why This Matters:
Consider an investment with these annual returns:
- Year 1: +50%
- Year 2: -30%
- Year 3: +20%
Average Annual Return: (50 - 30 + 20) ÷ 3 = 13.33%
Actual CAGR: 9.59%
A $1,000 investment would actually grow to $1,323 (not $1,444 as the average suggests).
Practical Applications
CAGR is widely used across finance and business for various purposes:
Investment Performance Comparison
CAGR provides a standardized way to compare investments with different time horizons and volatility profiles. Whether comparing stocks, bonds, mutual funds, or real estate investments, CAGR levels the playing field.
Business Growth Analysis
Companies use CAGR to communicate growth in:
- Revenue growth over multiple years
- User base expansion
- Market share gains
- Profit growth trends
Personal Financial Planning
Individual investors use CAGR to:
- Evaluate portfolio performance
- Set realistic return expectations
- Calculate required growth rates for retirement goals
- Compare different investment strategies
Pro Tip: When evaluating mutual funds or ETFs, always look at the CAGR over multiple time periods (3-year, 5-year, 10-year) rather than just annual returns to get a better picture of consistent performance.
Limitations of CAGR
While CAGR is a powerful metric, it has important limitations you should understand:
1. Assumes Smooth Growth
CAGR presents growth as if it happened evenly over time, which rarely occurs in reality. An investment with 10% CAGR might have had years of 30% gains and 20% losses.
2. Ignores Volatility
Two investments with the same CAGR can have vastly different risk profiles. CAGR doesn't capture the bumpy ride along the way.
3. No Cash Flow Consideration
CAGR assumes no money is added or withdrawn during the investment period. It can't accurately represent returns when you're making regular contributions or withdrawals.
4. Vulnerable to Manipulation
By carefully selecting start and end dates, CAGR can be manipulated to show better or worse performance than typical.
Warning: Never rely solely on CAGR when making investment decisions. Always consider it alongside other metrics like standard deviation, maximum drawdown, and Sharpe ratio for a complete picture.
5. Not Suitable for Short Periods
CAGR becomes less meaningful for periods shorter than one year, as it annualizes returns that haven't actually lasted a full year.
Frequently Asked Questions
What is a good CAGR for stocks?
Historically, the S&P 500 has delivered a CAGR of approximately 10-11% over the long term. A CAGR above this benchmark is generally considered good, though it depends on the risk taken and the time period measured.
How is CAGR different from IRR?
Internal Rate of Return (IRR) accounts for multiple cash flows at different times, while CAGR only considers the beginning and ending values. IRR is more complex but more accurate for investments with irregular cash flows.
Can CAGR be negative?
Yes, CAGR can be negative if the ending value is less than the beginning value, indicating the investment lost value over the period measured.
How do I use CAGR for retirement planning?
Use CAGR to estimate how much your investments need to grow annually to reach your retirement goals. For example, if you need to grow $100,000 to $500,000 in 20 years, you'd need a CAGR of about 8.4%.
Is higher CAGR always better?
Not necessarily. Higher CAGR often comes with higher risk and volatility. It's important to consider your risk tolerance and investment timeline when evaluating CAGR.
How often should I calculate CAGR for my portfolio?
Review your portfolio's CAGR annually, but focus on longer periods (3+ years) for meaningful insights. Short-term CAGR can be misleading due to market volatility.
Disclaimer: This article is for educational purposes only and should not be considered investment advice. Always conduct your own research and consult with qualified financial advisors before making investment decisions.